DRIDmetric

DRIDmetric is a Python package to calculate the first three moments of the Distribution of Reciprocal Interatomic Distances (DRID) for molecular dynamics (MD) trajectories.

The DRID representation is a structure-preserving dimensionality reduction method that captures essential kinetic and structural information, making it highly suitable for clustering, free energy landscape analysis, and kinetic modeling.

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Features

• Compute frame-wise DRID vectors from MD trajectories
• Based on reciprocal interatomic distances to emphasize short-range contacts
• Extract first three moments of distance distributions for selected centroids:
  • Mean (μ)
  • Variance (ν)
  • Skewness (ξ)
• Simple integration with MDAnalysis
• Outputs results as NumPy arrays for direct use in clustering or ML pipelines

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Mathematical Definition

Given:

• a set of m centroids $C={c_i}_{i=1}^m$,
• a set of N reference atoms $A={a_j}_{j=1}^{N}$, excluding covalently bound neighbors,

the distribution of reciprocal distances is defined by:

$$ d_{ij} = | c_i - a_j |, \quad \text{with reciprocal } \frac{1}{d_{ij}} $$

The first three moments for centroid (i) are:

$$ \mu_i = \frac{1}{N-1-n_b^i} \sum_j \frac{1}{d_{ij}} $$

$$ \nu_i = \left[ \frac{1}{N-1-n_b^i} \sum_j \frac{1}{(d_{ij}-\mu_i)^2} \right]^{1/2} $$

$$ \xi_i = \left[ \frac{1}{N-1-n_b^i} \sum_j \frac{1}{(d_{ij}-\mu_i)^3} \right]^{1/3} $$

where $ n_b^i $ is the number of covalent bonds for centroid $c_i$.

The DRID vector of a frame is then a 3m-dimensional vector:

$$ (\mu_1,\nu_1,\xi_1,;\ldots,;\mu_m,\nu_m,\xi_m) $$

The distance metric between two conformations $j$ and $k$ in DRID space is:

$$ s_{jk} = \frac{1}{3m} \sum_{i=1}^m \left[ (\mu_i^j-\mu_i^k)^2 + (\nu_i^j-\nu_i^k)^2 + (\xi_i^j-\xi_i^k)^2 \right]^{1/2} $$

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Installation

Install directly within your environment

pip install git+http://github.com/MoSchaeffler/DRIDmetric.git#egg=DRIDmetric

or clone and install in editable mode

git clone https://github.com/MoSchaeffler/DRIDmetric.git
cd DRIDmetric
pip install -e .

This installs:

• numpy
• tqdm
• MDAnalysis

DRID class

from DRIDmetric import DRID

DRID(
    top: str,
    traj: str,
    atom_selection: str,
    centroid_selection: str,
)

Parameters

• top (str)
  Topology file (e.g., .gro, .tpr, .pdb, …).

• traj (str)
  Trajectory file (e.g., .xtc, .trr, .dcd, …).

• centroid_selection (str)
  MDAnalysis selection string defining centroid atoms, e.g.:
  "(name CA and resid 28) or (name CA and resid 23) or (name CA and resid 1) ..."

• atom_selection (str)
  MDAnalysis selection string for the reference atom group (atoms compared to the centroids), e.g.:
  "protein"

Notes
• Covalently bonded neighbors of each centroid are automatically excluded from its reference set.
• The class iterates frames of traj, computing ((\mu,\nu,\xi)) per centroid and saving an array of shape (n_frames, n_centroids, 3).

Methods

• run(outname: str = "DRID") -> np.array
  Computes DRID for all frames and saves a NumPy file outname.npy.

Usage

Minimal Example

from DRIDmetric import DRID

# Input files
top = "/path/to/your/topology.tpr"
traj = "/path/to/your/trajectory.xtc"

# MDAnalysis selections
sel_atoms = "protein"
sel_cent  = "(name CA and resid 1) or (name CA and resid 11) or (name CA and resid 21)"

drid = DRID(top, traj, sel_atoms, sel_cent)
drid.run("DRID_output")

Please refer to the example for detailed usage instructions

Reference

If you use this package, please cite:

• Schäffler, Wales, & Strodel (2024) Chem. Commun.
  “The energy landscape of Aβ42: a funnel to disorder for the monomer becomes a folding funnel for self-assembly.”

Background on DRID:

• Zhou & Caflisch (2012) J. Chem. Theory Comput.
• Chakraborty, Straub & Thirumalai (2023) Sci. Adv.